An algorithm for sparse MRI reconstruction by Schatten p-norm minimization

MEDL-Net: A model-based neural network for MRI reconstruction with enhanced deep learned regularizers

PURPOSE

To improve the MRI reconstruction performance of model-based networks and to alleviate their large demand for GPU memory.

METHODS

A model-based neural network with enhanced deep learned regularizers (MEDL-Net) was proposed. The MEDL-Net is separated into several submodules, each of which consists of several cascades to mimic the optimization steps in conventional MRI reconstruction algorithms. Information from shallow cascades is densely connected to latter ones to enrich their inputs in each submodule, and additional revising blocks (RB) are stacked at the end of the submodules to bring more flexibility. Moreover, a composition loss function was designed to explicitly supervise RBs.

RESULTS

Network performance was evaluated on a publicly available dataset. The MEDL-Net quantitatively outperforms the state-of-the-art methods on different MR image sequences with different acceleration rates (four-fold and six-fold). Moreover, the reconstructed images showed that the detailed textures are better preserved. In addition, fewer cascades are required when achieving the same reconstruction results compared with other model-based networks.

CONCLUSION

In this study, a more efficient model-based deep network was proposed to reconstruct MR images. The experimental results indicate that the proposed method improves reconstruction performance with fewer cascades, which alleviates the large demand for GPU memory.

The extent of algorithm aversion in decision-making situations with varying gravity

Algorithms already carry out many tasks more reliably than human experts. Nevertheless, some subjects have an aversion towards algorithms. In some decision-making situations an error can have serious consequences, in others not. In the context of a framing experiment, we examine the connection between the consequences of a decision-making situation and the frequency of algorithm aversion. This shows that the more serious the consequences of a decision are, the more frequently algorithm aversion occurs. Particularly in the case of very important decisions, algorithm aversion thus leads to a reduction of the probability of success. This can be described as the tragedy of algorithm aversion.

Systematic Analysis and Review of Magnetic Resonance Imaging (MRI) Reconstruction Techniques

BACKGROUND

Magnetic Resonance Imaging (MRI) plays an important role in the field of medical diagnostic imaging as it poses non-invasive acquisition and high soft-tissue contrast. However, a huge time is needed for the MRI scanning process that results in motion artifacts, degrades image quality, misinterprets the data, and may cause discomfort to the patient. Thus, the main goal of MRI research is to accelerate data acquisition processing without affecting the quality of the image.

INTRODUCTION

This paper presents a survey based on distinct conventional MRI reconstruction methodologies. In addition, a novel MRI reconstruction strategy is proposed based on weighted Compressive Sensing (CS), Penalty-aided minimization function, and Meta-heuristic optimization technique.

METHODS

An illustrative analysis is done concerning adapted methods, datasets used, execution tools, performance measures, and values of evaluation metrics. Moreover, the issues of existing methods and the research gaps considering conventional MRI reconstruction schemes are elaborated to obtain improved contribution for devising significant MRI reconstruction techniques.

RESULTS

The proposed method will reduce conventional aliasing artifact problems, may attain lower Mean Square Error (MSE), higher Peak Signal-to-Noise Ratio (PSNR), and Structural SIMilarity (SSIM) index.

CONCLUSION

The issues of existing methods and the research gaps considering conventional MRI reconstruction schemes are elaborated to devising an improved significant MRI reconstruction technique.

Calibrationless parallel imaging reconstruction for multislice MR data using low-rank tensor completion

PURPOSE

To provide joint calibrationless parallel imaging reconstruction of highly accelerated multislice 2D MR k-space data.

METHODS

Adjacent image slices in multislice MR data have similar coil sensitivity maps, spatial support, and image content. Such similarities can be utilized to improve image quality by reconstructing multiple slices jointly with low-rank tensor completion. Specifically, the multichannel k-space data from multiple slices are constructed into a block-wise Hankel tensor and iteratively updated by promoting tensor low-rankness through higher-order SVD. This multislice block-wise Hankel tensor completion was implemented for 2D spiral and Cartesian k-space undersampling where sampling patterns vary between adjacent slices. The approach was evaluated with human brain MR data and compared to the traditional single-slice simultaneous autocalibrating and k-space estimation reconstruction.

RESULTS

The proposed multislice block-wise Hankel tensor completion approach robustly reconstructed highly undersampled multislice 2D spiral and Cartesian data. It produced substantially lower level of artifacts compared to the traditional single-slice simultaneous autocalibrating and k-space estimation reconstruction. Quantitative evaluation using error maps and root mean square error demonstrated its significantly improved performance in terms of residual artifacts and root mean square error.

CONCLUSION

Our proposed multislice block-wise Hankel tensor completion method exploits the similar coil sensitivity and image content within multislice MR data through a tensor completion framework. It offers a new and effective approach to acquire and reconstruct highly undersampled multislice MR data in a calibrationless manner.

A Unified Scalable Equivalent Formulation for Schatten Quasi-Norms

The Schatten quasi-norm is an approximation of the rank, which is tighter than the nuclear norm. However, most Schatten quasi-norm minimization (SQNM) algorithms suffer from high computational cost to compute the singular value decomposition (SVD) of large matrices at each iteration. In this paper, we prove that for any p, p1, p2>0 satisfying 1/p=1/p1+1/p2, the Schatten p-(quasi-)norm of any matrix is equivalent to minimizing the product of the Schatten p1-(quasi-)norm and Schatten p2-(quasi-)norm of its two much smaller factor matrices. Then, we present and prove the equivalence between the product and its weighted sum formulations for two cases: p1=p2 and p1≠p2. In particular, when p>1/2, there is an equivalence between the Schatten p-quasi-norm of any matrix and the Schatten 2p-norms of its two factor matrices. We further extend the theoretical results of two factor matrices to the cases of three and more factor matrices, from which we can see that for any 0<p<1, the Schatten p-quasi-norm of any matrix is the minimization of the mean of the Schatten (⌊1/p⌋+1)p-norms of ⌊1/p⌋+1 factor matrices, where ⌊1/p⌋ denotes the largest integer not exceeding 1/p.

An Algorithm Combining Analysis-based Blind Compressed Sensing and Nonlocal Low-rank Constraints for MRI Reconstruction

BACKGROUND

In order to overcome the limitation of long scanning time, compressive sensing (CS) technology exploits the sparsity of image in some transform domain to reduce the amount of acquired data. Therefore, CS has been widely used in magnetic resonance imaging (MRI) reconstruction.

DISCUSSION

Blind compressed sensing enables to recover the image successfully from highly under- sampled measurements, because of the data-driven adaption of the unknown transform basis priori. Moreover, analysis-based blind compressed sensing often leads to more efficient signal reconstruction with less time than synthesis-based blind compressed sensing. Recently, some experiments have shown that nonlocal low-rank property has the ability to preserve the details of the image for MRI reconstruction.

METHODS

Here, we focus on analysis-based blind compressed sensing, and combine it with additional nonlocal low-rank constraint to achieve better MR images from fewer measurements. Instead of nuclear norm, we exploit non-convex Schatten p-functionals for the rank approximation.

RESULTS & CONCLUSION

Simulation results indicate that the proposed approach performs better than the previous state-of-the-art algorithms.

PEC-GRAPPA reconstruction of simultaneous multislice EPI with slice-dependent 2D Nyquist ghost correction

PURPOSE

To provide simultaneous multislice (SMS) EPI reconstruction with k-space implementation and robust Nyquist ghost correction.

METHODS

2D phase error correction SENSE (PEC-SENSE) was recently developed for Nyquist ghost correction in SMS EPI reconstruction for which virtual coil simultaneous autocalibration and k-space estimation (VC-SAKE) was used to remove slice-dependent Nyquist ghosts and intershot 2D phase variations in multi-shot EPI reference scan. However, masking coil sensitivity maps to exclude background region in PEC-SENSE and manually selecting slice-wise target ranks in VC-SAKE are cumbersome procedures in practice. To avoid masking, the concept of PEC-SENSE is extended to k-space implementation and termed as PEC-GRAPPA. Furthermore, a singular value shrinkage scheme is incorporated in VC-SAKE to circumvent the empirical slice-wise target rank selection. PEC-GRAPPA was evaluated and compared to PEC-SENSE with/without masking and 1D linear phase correction GRAPPA.

RESULTS

PEC-GRAPPA robustly reconstructed SMS EPI images from 7T phantom and human brain data, effectively removing the phase error-induced artifacts. The resulting residual artifact level and temporal SNR were comparable to those by PEC-SENSE with careful tuning. PEC-GRAPPA outperformed PEC-SENSE without masking and 1D linear phase correction GRAPPA.

CONCLUSION

Our proposed PEC-GRAPPA approach effectively removes the artifacts caused by Nyquist ghosts in SMS EPI without cumbersome tuning. This approach provides a robust and practical implementation of SMS EPI reconstruction in k-space with slice-dependent 2D Nyquist ghost correction.

Reconstruction of Undersampled Big Dynamic MRI Data Using Non-Convex Low-Rank and Sparsity Constraints

Dynamic magnetic resonance imaging (MRI) has been extensively utilized for enhancing medical living environment visualization, however, in clinical practice it often suffers from long data acquisition times. Dynamic imaging essentially reconstructs the visual image from raw (k,t)-space measurements, commonly referred to as big data. The purpose of this work is to accelerate big medical data acquisition in dynamic MRI by developing a non-convex minimization framework. In particular, to overcome the inherent speed limitation, both non-convex low-rank and sparsity constraints were combined to accelerate the dynamic imaging. However, the non-convex constraints make the dynamic reconstruction problem difficult to directly solve through the commonly-used numerical methods. To guarantee solution efficiency and stability, a numerical algorithm based on Alternating Direction Method of Multipliers (ADMM) is proposed to solve the resulting non-convex optimization problem. ADMM decomposes the original complex optimization problem into several simple sub-problems. Each sub-problem has a closed-form solution or could be efficiently solved using existing numerical methods. It has been proven that the quality of images reconstructed from fewer measurements can be significantly improved using non-convex minimization. Numerous experiments have been conducted on two in vivo cardiac datasets to compare the proposed method with several state-of-the-art imaging methods. Experimental results illustrated that the proposed method could guarantee the superior imaging performance in terms of quantitative and visual image quality assessments.

Sparse and dense hybrid representation via subspace modeling for dynamic MRI

Recent theoretical results on compressed sensing and low-rank matrix recovery have inspired significant interest in joint sparse and low rank modeling of dynamic magnetic resonance imaging (dMRI). Existing approaches usually describe these two respective prior information with different formulations. In this paper, we present a novel sparse and dense hybrid representation (SDR) model which describes the sparse plus low rank properties by a unified way. More specifically, under the learned dictionary consisting of temporal basis functions, SDR models the spatial coefficients in two subspaces with Laplacian and Gaussian prior distributions, respectively. This results in the objective function consisting of L1-L2 hybrid penalty term for the coefficients and Frobenius norm term for the dictionary. An efficient algorithm utilizing alternating direction technique is developed to solve the proposed model. Extensive experiments under a variety of test images and a comprehensive evaluation against existing state-of-the-art methods consistently demonstrate the potential of the proposed model and algorithm, in terms of reconstruction and separation comparisons.

Dynamic MRI reconstruction from highly undersampled (k, t)-space data using weighted Schatten p-norm regularizer of tensor

Combination of the low-rankness and sparsity has been successfully used to reconstruct desired dynamic magnetic resonance image (MRI) from highly-undersampled (k, t)-space data. However, nuclear norm, as a convex relaxation of the rank function, can cause the solution deviating from the original solution of low-rank problem. Moreover, equally treating different rank component is not flexible to deal with real applications. In this paper, an efficient reconstruction model is proposed to efficiently reconstruct dynamic MRI. First, we treat dynamic MRI as a 3rd-order tensor, and formulate the low-rankness via non-convex Schatten p-norm of matrices unfolded from the tensor. Secondly, we assign different weight for each rank component in Schatten p-norm. Furthermore, we combine the proposed weighted Schatten p-norm of a tensor as low-rank regularizer, and spatiotemporal total variation as sparse regularizer to formulate the reconstruction model for dynamic MRI. Thirdly, to efficiently solve the formulated reconstruction model, we derive an algorithm based on Bregman iterations with alternating direction multiplier. Over two public data sets of dynamic MRI, experiments demonstrate that the proposed method achieves much better quality.

Computationally efficient error estimate for evaluation of regularization in photoacoustic tomography

The model-based image reconstruction techniques for photoacoustic (PA) tomography require an explicit regularization. An error estimate (?2) minimization-based approach was proposed and developed for the determination of a regularization parameter for PA imaging. The regularization was used within Lanczos bidiagonalization framework, which provides the advantage of dimensionality reduction for a large system of equations. It was shown that the proposed method is computationally faster than the state-of-the-art techniques and provides similar performance in terms of quantitative accuracy in reconstructed images. It was also shown that the error estimate (?2) can also be utilized in determining a suitable regularization parameter for other popular techniques such as Tikhonov, exponential, and nonsmooth (?1 and total variation norm based) regularization methods.

MRI reconstruction of multi-image acquisitions using a rank regularizer with data reordering

PURPOSE

To improve rank constrained reconstructions for undersampled multi-image MRI acquisitions.

METHODS

Motivated by the recent developments in low-rank matrix completion theory and its applicability to rapid dynamic MRI, a new reordering-based rank constrained reconstruction of undersampled multi-image data that uses prior image information is proposed. Instead of directly minimizing the nuclear norm of a matrix of estimated images, the nuclear norm of reordered matrix values is minimized. The reordering is based on the prior image estimates. The method is tested on brain diffusion imaging data and dynamic contrast enhanced myocardial perfusion data.

RESULTS

Good quality images from data undersampled by a factor of three for diffusion imaging and by a factor of 3.5 for dynamic cardiac perfusion imaging with respiratory motion were obtained. Reordering gave visually improved image quality over standard nuclear norm minimization reconstructions. Root mean squared errors with respect to ground truth images were improved by ∼18% and ∼16% with reordering for diffusion and perfusion applications, respectively.

CONCLUSIONS

The reordered low-rank constraint is a way to inject prior image information that offers improvements over a standard low-rank constraint for undersampled multi-image MRI reconstructions.

Accelerated cardiac cine MRI using locally low rank and finite difference constraints

PURPOSE

To evaluate the potential value of combining multiple constraints for highly accelerated cardiac cine MRI.

METHODS

A locally low rank (LLR) constraint and a temporal finite difference (FD) constraint were combined to reconstruct cardiac cine data from highly undersampled measurements. Retrospectively undersampled 2D Cartesian reconstructions were quantitatively evaluated against fully-sampled data using normalized root mean square error, structural similarity index (SSIM) and high frequency error norm (HFEN). This method was also applied to 2D golden-angle radial real-time imaging to facilitate single breath-hold whole-heart cine (12 short-axis slices, 9-13s single breath hold). Reconstruction was compared against state-of-the-art constrained reconstruction methods: LLR, FD, and k-t SLR.

RESULTS

At 10 to 60 spokes/frame, LLR+FD better preserved fine structures and depicted myocardial motion with reduced spatio-temporal blurring in comparison to existing methods. LLR yielded higher SSIM ranking than FD; FD had higher HFEN ranking than LLR. LLR+FD combined the complimentary advantages of the two, and ranked the highest in all metrics for all retrospective undersampled cases. Single breath-hold multi-slice cardiac cine with prospective undersampling was enabled with in-plane spatio-temporal resolutions of 2×2mm(2) and 40ms.

CONCLUSION

Highly accelerated cardiac cine is enabled by the combination of 2D undersampling and the synergistic use of LLR and FD constraints.

Accelerating patch-based directional wavelets with multicore parallel computing in compressed sensing MRI

Compressed sensing MRI (CS-MRI) is a promising technology to accelerate magnetic resonance imaging. Both improving the image quality and reducing the computation time are important for this technology. Recently, a patch-based directional wavelet (PBDW) has been applied in CS-MRI to improve edge reconstruction. However, this method is time consuming since it involves extensive computations, including geometric direction estimation and numerous iterations of wavelet transform. To accelerate computations of PBDW, we propose a general parallelization of patch-based processing by taking the advantage of multicore processors. Additionally, two pertinent optimizations, excluding smooth patches and pre-arranged insertion sort, that make use of sparsity in MR images are also proposed. Simulation results demonstrate that the acceleration factor with the parallel architecture of PBDW approaches the number of central processing unit cores, and that pertinent optimizations are also effective to make further accelerations. The proposed approaches allow compressed sensing MRI reconstruction to be accomplished within several seconds.

Variable density incoherent spatiotemporal acquisition (VISTA) for highly accelerated cardiac MRI

PURPOSE

For the application of compressive sensing to parallel MRI, Poisson disk sampling (PDS) has been shown to generate superior results compared with random sampling methods. However, due to its limited flexibility to incorporate additional constraints, PDS is not readily extendible to dynamic applications. Here, we propose and validate a pseudo-random sampling technique that allows incorporating constraints specific to dynamic imaging.

METHODS

The proposed sampling scheme, called variable density incoherent spatiotemporal acquisition (VISTA), is based on constrained minimization of Riesz energy on a spatiotemporal grid. Data from both a digital phantom and real-time cine were used to compare VISTA with uniform interleaved sampling (UIS) and variable density random sampling (VRS). The image quality was assessed qualitatively and quantitatively.

RESULTS

VISTA improved the trade-off between noise and sharpness. Also, VISTA produced diagnostic quality images at an acceleration rate of 15, whereas UIS and VRS images degraded below the diagnostic threshold at lower acceleration rates.

CONCLUSIONS

VISTA generates spatiotemporal sampling patterns with high levels of uniformity and incoherence, while maintaining a constant temporal resolution. Using a small pilot study, VISTA was shown to produce diagnostic quality images at acceleration rates up to 15.

Motion-compensated compressed sensing for dynamic contrast-enhanced MRI using regional spatiotemporal sparsity and region tracking: block low-rank sparsity with motion-guidance (BLOSM)

PURPOSE

Dynamic contrast-enhanced MRI of the heart is well-suited for acceleration with compressed sensing (CS) due to its spatiotemporal sparsity; however, respiratory motion can degrade sparsity and lead to image artifacts. We sought to develop a motion-compensated CS method for this application.

METHODS

A new method, Block LOw-rank Sparsity with Motion-guidance (BLOSM), was developed to accelerate first-pass cardiac MRI, even in the presence of respiratory motion. This method divides the images into regions, tracks the regions through time, and applies matrix low-rank sparsity to the tracked regions. BLOSM was evaluated using computer simulations and first-pass cardiac datasets from human subjects. Using rate-4 undersampling, BLOSM was compared with other CS methods such as k-t SLR that uses matrix low-rank sparsity applied to the whole image dataset, with and without motion tracking, and to k-t FOCUSS with motion estimation and compensation that uses spatial and temporal-frequency sparsity.

RESULTS

BLOSM was qualitatively shown to reduce respiratory artifact compared with other methods. Quantitatively, using root mean squared error and the structural similarity index, BLOSM was superior to other methods.

CONCLUSION

BLOSM, which exploits regional low-rank structure and uses region tracking for motion compensation, provides improved image quality for CS-accelerated first-pass cardiac MRI.

A photoacoustic image reconstruction method using total variation and nonconvex optimization

Background

In photoacoustic imaging (PAI), the reduction of scanning time is a major concern for PAI in practice. A popular strategy is to reconstruct the image from the sparse-view sampling data. However, the insufficient data leads to reconstruction quality deteriorating. Therefore, it is very important to enhance the quality of the sparse-view reconstructed images.

Method

In this paper, we proposed a joint total variation and L_p-norm (TV-L_p) based image reconstruction algorithm for PAI. In this algorithm, the reconstructed image is updated by calculating its total variation value and L_p-norm value. Along with the iteration, an operator-splitting framework is utilized to reduce the computational cost and the Barzilai-Borwein step size selection method is adopted to obtain the faster convergence.

Results and conclusion

Through the numerical simulation, the proposed algorithm is validated and compared with other widely used PAI reconstruction algorithms. It is revealed in the simulation result that the proposed algorithm may be more accurate than the other algorithms. Moreover, the computational cost, the convergence, the robustness to noises and the tunable parameters of the algorithm are all discussed respectively. We also implement the TV-L_p algorithm in the in-vitro experiments to verify its performance in practice. Through the numerical simulations and in-vitro experiments, it is demonstrated that the proposed algorithm enhances the quality of the reconstructed images with faster calculation speed and convergence.

Multidimensional compressed sensing MRI using tensor decomposition-based sparsifying transform

Compressed Sensing (CS) has been applied in dynamic Magnetic Resonance Imaging (MRI) to accelerate the data acquisition without noticeably degrading the spatial-temporal resolution. A suitable sparsity basis is one of the key components to successful CS applications. Conventionally, a multidimensional dataset in dynamic MRI is treated as a series of two-dimensional matrices, and then various matrix/vector transforms are used to explore the image sparsity. Traditional methods typically sparsify the spatial and temporal information independently. In this work, we propose a novel concept of tensor sparsity for the application of CS in dynamic MRI, and present the Higher-order Singular Value Decomposition (HOSVD) as a practical example. Applications presented in the three- and four-dimensional MRI data demonstrate that HOSVD simultaneously exploited the correlations within spatial and temporal dimensions. Validations based on cardiac datasets indicate that the proposed method achieved comparable reconstruction accuracy with the low-rank matrix recovery methods and, outperformed the conventional sparse recovery methods.

k-t acceleration in pure phase encode MRI to monitor dynamic flooding processes in rock core plugs

Monitoring the pore system in sedimentary rocks with MRI when fluids are introduced is very important in the study of petroleum reservoirs and enhanced oil recovery. However, the lengthy acquisition time of each image, with pure phase encode MRI, limits the temporal resolution. Spatiotemporal correlations can be exploited to undersample the k-t space data. The stacked frames/profiles can be well approximated by an image matrix with rank deficiency, which can be recovered by nonlinear nuclear norm minimization. Sparsity of the x-t image can also be exploited for nonlinear reconstruction. In this work the results of a low rank matrix completion technique were compared with k-t sparse compressed sensing. These methods are demonstrated with one dimensional SPRITE imaging of a Bentheimer rock core plug and SESPI imaging of a Berea rock core plug, but can be easily extended to higher dimensionality and/or other pure phase encode measurements. These ideas will enable higher dimensionality pure phase encode MRI studies of dynamic flooding processes in low magnetic field systems.

Enhancement of the low resolution image quality using randomly sampled data for multi-slice MR imaging

Low resolution images are often acquired in in vivo MR applications involving in large field-of-view (FOV) and high speed imaging, such as, whole-body MRI screening and functional MRI applications. In this work, we investigate a multi-slice imaging strategy for acquiring low resolution images by using compressed sensing (CS) MRI to enhance the image quality without increasing the acquisition time. In this strategy, low resolution images of all the slices are acquired using multiple-slice imaging sequence. In addition, extra randomly sampled data in one center slice are acquired by using the CS strategy. These additional randomly sampled data are multiplied by the weighting functions generated from low resolution full k-space images of the two slices, and then interpolated into the k-space of other slices. In vivo MR images of human brain were employed to investigate the feasibility and the performance of the proposed method. Quantitative comparison between the conventional low resolution images and those from the proposed method was also performed to demonstrate the advantage of the method.

Low-rank modeling of local k-space neighborhoods (LORAKS) for constrained MRI

Recent theoretical results on low-rank matrix reconstruction have inspired significant interest in low-rank modeling of MRI images. Existing approaches have focused on higher-dimensional scenarios with data available from multiple channels, timepoints, or image contrasts. The present work demonstrates that single-channel, single-contrast, single-timepoint k-space data can also be mapped to low-rank matrices when the image has limited spatial support or slowly varying phase. Based on this, we develop a novel and flexible framework for constrained image reconstruction that uses low-rank matrix modeling of local k-space neighborhoods (LORAKS). A new regularization penalty and corresponding algorithm for promoting low-rank are also introduced. The potential of LORAKS is demonstrated with simulated and experimental data for a range of denoising and sparse-sampling applications. LORAKS is also compared against state-of-the-art methods like homodyne reconstruction, l1-norm minimization, and total variation minimization, and is demonstrated to have distinct features and advantages. In addition, while calibration-based support and phase constraints are commonly used in existing methods, the LORAKS framework enables calibrationless use of these constraints.

Accelerating dynamic magnetic resonance imaging (MRI) for lung tumor tracking based on low-rank decomposition in the spatial-temporal domain: a feasibility study based on simulation and preliminary prospective undersampled MRI

PURPOSE

To evaluate a low-rank decomposition method to reconstruct down-sampled k-space data for the purpose of tumor tracking.

METHODS AND MATERIALS

Seven retrospective lung cancer patients were included in the simulation study. The fully-sampled k-space data were first generated from existing 2-dimensional dynamic MR images and then down-sampled by 5 × -20 × before reconstruction using a Cartesian undersampling mask. Two methods, a low-rank decomposition method using combined dynamic MR images (k-t SLR based on sparsity and low-rank penalties) and a total variation (TV) method using individual dynamic MR frames, were used to reconstruct images. The tumor trajectories were derived on the basis of autosegmentation of the resultant images. To further test its feasibility, k-t SLR was used to reconstruct prospective data of a healthy subject. An undersampled balanced steady-state free precession sequence with the same undersampling mask was used to acquire the imaging data.

RESULTS

In the simulation study, higher imaging fidelity and low noise levels were achieved with the k-t SLR compared with TV. At 10 × undersampling, the k-t SLR method resulted in an average normalized mean square error <0.05, as opposed to 0.23 by using the TV reconstruction on individual frames. Less than 6% showed tracking errors >1 mm with 10 × down-sampling using k-t SLR, as opposed to 17% using TV. In the prospective study, k-t SLR substantially reduced reconstruction artifacts and retained anatomic details.

CONCLUSIONS

Magnetic resonance reconstruction using k-t SLR on highly undersampled dynamic MR imaging data results in high image quality useful for tumor tracking. The k-t SLR was superior to TV by better exploiting the intrinsic anatomic coherence of the same patient. The feasibility of k-t SLR was demonstrated by prospective imaging acquisition and reconstruction.

Calibrationless parallel magnetic resonance imaging: a joint sparsity model

State-of-the-art parallel MRI techniques either explicitly or implicitly require certain parameters to be estimated, e.g., the sensitivity map for SENSE, SMASH and interpolation weights for GRAPPA, SPIRiT. Thus all these techniques are sensitive to the calibration (parameter estimation) stage. In this work, we have proposed a parallel MRI technique that does not require any calibration but yields reconstruction results that are at par with (or even better than) state-of-the-art methods in parallel MRI. Our proposed method required solving non-convex analysis and synthesis prior joint-sparsity problems. This work also derives the algorithms for solving them. Experimental validation was carried out on two datasets-eight channel brain and eight channel Shepp-Logan phantom. Two sampling methods were used-Variable Density Random sampling and non-Cartesian Radial sampling. For the brain data, acceleration factor of 4 was used and for the other an acceleration factor of 6 was used. The reconstruction results were quantitatively evaluated based on the Normalised Mean Squared Error between the reconstructed image and the originals. The qualitative evaluation was based on the actual reconstructed images. We compared our work with four state-of-the-art parallel imaging techniques; two calibrated methods-CS SENSE and l1SPIRiT and two calibration free techniques-Distributed CS and SAKE. Our method yields better reconstruction results than all of them.

Interpolated compressed sensing for 2D multiple slice fast MR imaging

Sparse MRI has been introduced to reduce the acquisition time and raw data size by undersampling the k-space data. However, the image quality, particularly the contrast to noise ratio (CNR), decreases with the undersampling rate. In this work, we proposed an interpolated Compressed Sensing (iCS) method to further enhance the imaging speed or reduce data size without significant sacrifice of image quality and CNR for multi-slice two-dimensional sparse MR imaging in humans. This method utilizes the k-space data of the neighboring slice in the multi-slice acquisition. The missing k-space data of a highly undersampled slice are estimated by using the raw data of its neighboring slice multiplied by a weighting function generated from low resolution full k-space reference images. In-vivo MR imaging in human feet has been used to investigate the feasibility and the performance of the proposed iCS method. The results show that by using the proposed iCS reconstruction method, the average image error can be reduced and the average CNR can be improved, compared with the conventional sparse MRI reconstruction at the same undersampling rate.

Compressed sensing based real-time dynamic MRI reconstruction

This work addresses the problem of real-time online reconstruction of dynamic magnetic resonance imaging sequences. The proposed method reconstructs the difference between the previous and the current image frames. This difference image is sparse. We recover the sparse difference image from its partial k-space scans by using a nonconvex compressed sensing algorithm. As there was no previous fast enough algorithm for real-time reconstruction, we derive a novel algorithm for this purpose. Our proposed method has been compared against state-of-the-art offline and online reconstruction methods. The accuracy of the proposed method is less than offline methods but noticeably higher than the online techniques. For real-time reconstruction we are also concerned about the reconstruction speed. Our method is capable of reconstructing 128 × 128 images at the rate of 6 frames/s, 180 × 180 images at the rate of 5 frames/s and 256 × 256 images at the rate of 2.5 frames/s.

Exploiting rank deficiency and transform domain sparsity for MR image reconstruction

The reconstruction of magnetic resonance (MR) images from the partial samples of their k-space data using compressed sensing (CS)-based methods has generated a lot of interest in recent years. To reconstruct the MR images, these techniques exploit the sparsity of the image in a transform domain (wavelets, total variation, etc.). In a recent work, it has been shown that it is also possible to reconstruct MR images by exploiting their rank deficiency. In this work, it will be shown that, instead of exploiting the sparsity of the image or rank deficiency alone, better reconstruction results can be achieved by combining transform domain sparsity with rank deficiency. To reconstruct an MR image using its transform domain sparsity and its rank deficiency, this work proposes a combined l(1)-norm (of the transform coefficients) and nuclear norm (of the MR image matrix) minimization problem. Since such an optimization problem has not been encountered before, this work proposes and derives a first-order algorithm to solve it. The reconstruction results show that the proposed approach yields significant improvements, in terms of both visual quality as well as the signal to noise ratio, over previous works that reconstruct MR images either by exploiting rank deficiency or by the standard CS-based technique popularly known as the 'Sparse MRI.'

Accelerated dynamic MRI exploiting sparsity and low-rank structure: k-t SLR

We introduce a novel algorithm to reconstruct dynamic magnetic resonance imaging (MRI) data from under-sampled k-t space data. In contrast to classical model based cine MRI schemes that rely on the sparsity or banded structure in Fourier space, we use the compact representation of the data in the Karhunen Louve transform (KLT) domain to exploit the correlations in the dataset. The use of the data-dependent KL transform makes our approach ideally suited to a range of dynamic imaging problems, even when the motion is not periodic. In comparison to current KLT-based methods that rely on a two-step approach to first estimate the basis functions and then use it for reconstruction, we pose the problem as a spectrally regularized matrix recovery problem. By simultaneously determining the temporal basis functions and its spatial weights from the entire measured data, the proposed scheme is capable of providing high quality reconstructions at a range of accelerations. In addition to using the compact representation in the KLT domain, we also exploit the sparsity of the data to further improve the recovery rate. Validations using numerical phantoms and in vivo cardiac perfusion MRI data demonstrate the significant improvement in performance offered by the proposed scheme over existing methods.